Adaptive wireless millirobotic locomotion into distal vasculature

Microcatheters have enabled diverse minimally invasive endovascular operations and notable health benefits compared with open surgeries. However, with tortuous routes far from the arterial puncture site, the distal vascular regions remain challenging for safe catheter access. Therefore, we propose a wireless stent-shaped magnetic soft robot to be deployed, actively navigated, used for medical functions, and retrieved in the example M4 segment of the middle cerebral artery. We investigate shape-adaptively controlled locomotion in phantoms emulating the physiological conditions here, where the lumen diameter shrinks from 1.5 mm to 1 mm, the radius of curvature of the tortuous lumen gets as small as 3 mm, the lumen bifurcation angle goes up to 120°, and the pulsatile flow speed reaches up to 26 cm/s. The robot can also withstand the flow when the magnetic actuation is turned off. These locomotion capabilities are confirmed in porcine arteries ex vivo. Furthermore, variants of the robot could release the tissue plasminogen activator on-demand locally for thrombolysis and function as flow diverters, initiating promising therapies towards acute ischemic stroke, aneurysm, arteriovenous malformation, dural arteriovenous fistulas, and brain tumors. These functions should facilitate the robot’s usage in new distal endovascular operations.

For all cases, the mass ratio between PDMS (base and crosslinker) and the NdFeB particles is 1:4.
The data are presented as mean values ± standard deviation for n = 3. b Modeling results on the (top view and side view). Both designs have the same body length and thickness. Therefore, the projection area Sp is the same when the robot is not deformed. When the helical-shaped robot is adaptive into the lumen with smaller Φl, the structure is stretched due to boundary constraint, and Sp is increased. In contrast, for the stent-shaped robot, due to the radial deformability, Sp is decreased. Scale bar: 1mm. b Variation of the Sp along with Φl. c Variation of Fdrag along with Φl.
The increasing of Sp notably increases Fdrag for the helical-shaped design, which further justifies the advantage of stent-shaped structure in flow withstanding. Due to the decreasing friction in arteries, the requirement on lmag_max can be much more relaxed. c Average speed of the robot vr for various translation speeds of the magnet vmag (fmag = 0.5 Hz, lmag = 55 mm). At vmag = 0.5 mm/s, where the robot can properly follow the magnet, the robot achieved the average speed vr at around 0.18 mm/s. Note that for higher vmag, vr can be increased, but the lagging is also more apparent. d Self-anchoring of the robot utilizing friction when the external magnetic field is off for porcine arteries. In a and c, the data are presented as mean values ± standard deviation for n = 5. The influence of vmag is much more significant than fmag. In a and b, the data are presented as mean values ± standard deviation for n = 3.

Supplementary Tables
Supplementary Table 1

Supplementary Note 1. Asymmetric friction-induced rolling
The permanent magnet-based robot manipulation leads to the asymmetric friction distributions on the robot along the " − " plane, which causes it to roll and induces the reaction force ")($* from the lumen. This behavior can be used for curved lumen traversing. As indicated in Supplementary   Figure 13a, the direction of the induced ")($* is decided by the magnet configuration, i.e., the rotation direction and the location relative to the robot (above or beneath).
To illustrate the mechanism, we use the example that the magnet is placed beneath the robot and rotates it around the positive side of the yr-axis (1 in Supplementary Figure 13a). We divide the robot into the upper and lower parts to explain the details of force relations, where the distributed forces are assumed to be centered for ease of illustration (Supplementary Figure 13b).
The equilibrium along the " -axis for the upper part can be represented as where +,,-is the normal force applied to the robot from the lumen wall, #+ is the inner force from the other part. In contrast, the force equilibrium for the lower part can be represented as Thus, the corresponding kinetic frictions along the " − " plane can be represented as !"#$,234+ = ∥ +,234+ cos( ) + ⊥ +,234+ sin( ), respectively. Thus, it is clear that !"#$,234+ > !"#$,,-, i.e., the friction on the lower interface (pointing to the positive " -axis) is greater than the one on the upper one (pointing to the negative " -axis) (1 in Supplementary Figure 13a). Thus, the robot tends to roll to the positive side of the " -axis such that the reaction force from the lumen wall ")($* balances the frictions along the "axis. The quantified !"#$,,-and !"#$,234+ are shown in Supplementary Figure 13c

Supplementary Note 2. Quantification of torques enabling the traversing among curved routes
Among the curved lumens (curved routes and bifurcations), three requirements need to be satisfied simultaneously to enable the traversing, i.e., 1) the maximum leading forces are greater than the maximum resistance forces (along the robot body-attached " -axis), 2) the maximum actuation torques around the " -axis are greater than the maximum resistance torques, 3) and the applied bending torques on the robot around the " -axis are greater than the minimum required torque to bend the robot into the desired curved routes. We regard the curved routes as the consecutive sequence of numerous straight lumen with infinitesimal length. Thus, the analyses of 1) and 2) can be referred directly from the straight lumen case, as explained in the main text. The following details will be about requirement 3).
The torques enabling the traversing of curved routes are composed of magnetic components, i.e., a) magnetic pulling force-based and b) direct magnetic torque-based, and c) the reaction-based from the lumen walls. Here we explain the modeling for each component.

Torque from the magnetic pulling force
There is always a pulling force /(0 on the robot pointing to the magnet's center when it leads the robot. /(0 induces a torque bending the robot towards route (c) -(d), as shown in Supplementary When the magnet is not leading the robot, /(0 is zero. Thus, the range of /(0_!3"$) is ]. This component is constant for curved routes with different radii of curvature $ .

Magnetic torque
Due to the reorientation and rotation of the magnet, there is a rotating vector of magnetic flux density along the ( − ( plane. This vector induces the magnetic torque /(0 , aligning the robot to the magnet (Supplementary Figure 14b). The maximum /(0 can be acquired when the magnet is not leading the robot, where the maximum flux density along the ( -axis is ?_/(? = 6.0 × 10 8= T. /(0 can then be computed as where " is the magnetic moment of the robot. The minimum Tmag can be acquired when the magnet leads the robot for 0.023 m, i.e., the maximum of Fmag is acquired. Here, the minimum flux density ?_/#+ = 4.9 × 10 8= T, then Thus, the range of /(0 is [6.3 × 10 8@ , 7.8 × 10 8@ ]. This component is uniform for curved routes with different $ .

Torque from the reaction force
When the robot starts to enter the curved route, the reaction force ")($* from the lumen wall is applied to the robot. As shown in Supplementary Figure 14c, as the robot rotates around the positive " -axis and tends to roll to the positive " -axis, ")($* points to the negative " -axis. The resultant torque ")($* bends the robot towards (c) -(d). For the simplification of illustration, the robot can be regarded as a cantilever beam to compute ")($* . First, by geometric approximation, the bending angle can be computed as where #+ is the length of robot into the curved routes. Meanwhile, based on the cantilever beam model, can be represented as where " is the second moment of area for the cross-section undergoing bending. Thus, the ")($* can be finally computed as Thus, this component is various for curved routes with different $ .
We first compare the magnet-based torques and /#+ , as shown in Supplementary Figure   14d. with the decreasing of $ (increasing of $ ), the gap between /#+ and the torques are more significant, which needs to be enabled by ")($* from the proper rotation direction of the robot.
where /(0 = 3.6 × 10 -4 N, at a distance of 0.023 m away from the robot in the global x-y plane. When the magnet is not leading the robot, /(0_!3"$) is zero.

Magnetic torque
/(0 is different among various bifurcation angles I (Supplementary Figure 15b). The maximum /(0 can be acquired when the magnet is not leading the robot, where the maximum flux density along the xa-axis is ?_/(? = 6.0 × 10 8= T. /(0 can be computed as The minimum Tmag can be acquired when the magnet leads the robot for 0.023 m, i.e., the maximum Fmag is acquired. Here, the minimum flux density ?_/#+ = 4.9 × 10 8= T,

Torque from the reaction force
When the robot starts to enter the bifurcation, the reaction force ")($* from the lumen wall is applied to the robot. As shown in Supplementary Figure 15c, when the robot rotates around the positive " -axis and tends to roll to the positive " -axis, ")($* points to the negative " -axis. The resultant torque ")($* also bends the robot towards (c) -(d). We also regard the robot as a cantilever beam to compute the ")($* here. First, the bending angle , i.e., = 0.5 I , can be represented as where #+ is the length of robot into the bifurcation junction. Then, based on the cantilever beam model, can be represented as Thus, the ")($* can be computed as To compute $ for the bifurcations, we have made the geometric analysis, and the following relation can be used, where 0(-is the bifurcation gap length (Supplementary Figure 15d). It can be seen that this component is also various for bifurcations with different I . Thus, ")($* can be finally computed We first quantify the magnet-based torques and compare them with /#+ , as shown in Supplementary Figure 15e. Note that with the increasing of I , the gap between /#+ and the magnet-based torques are more significant, which needs to be enabled by the ")($* from the proper rotation of the robot. Together with ")($* , the sum of these torques is superior to the /#+ among the physiologically relevant range, enabling the successful traversing among these routes (Supplementary Figure 15f). Certainly, these descriptive force modeling methods here are used to understand the basic underlying mechanics, and further finite element analyses will be carried out to explore the dynamics in future work. Note that the error bars indicate the maximum and minimum values. In e and f, the components of magnetic torques are represented as the average torque along the magnet movement ± half of the range for the achievable torque according to the force modeling.

Supplementary Note 4. Compatibility with the commercial microcatheters for distal arteries
An even smaller version of the robot, e.g., initial diameter Φr = 0.7 mm, compatible with the microcatheter for distal arteries, e.g., ID = 0.03 inch, could achieve retrievable locomotion for lumen diameter range Φl = 1.5 mm to 0.2 mm. Particularly, for Φl = 1.5 mm to 0.7 mm, the robot has no shape adaptation; for Φl = 0.7 mm to 0.2 mm, the robot is shape-adaptive during locomotion.
This claim was made through theoretical modeling in the previous response. To

Supplementary Note 5. Comparison with the standard neuro-interventional operations in distal arteries
As summarized in Supplementary Table S1, compared to the standard endovascular neurointerventional operations in the distal cortical arteries, our stent-shaped magnetic soft robots could be advantageous in the four following major aspects. We have conducted new experiments to confirm these superiorities: • Accessibility with self-anchoring capability: better controlled retrievable navigation among the targeted distally tortuous routes given flow or no flow; even for the highly curved route with the inclination angle of 180°; • Safety (in interaction forces): lower forces order (10 -4 -10 -2 N) applied to the vessel walls compared to standard methods (10 -1 -10 0 N); • Drug dosage: reduced dosages given local delivery to minimize the systematic side effect; • Adjustability: available to be adjusted as flow diverters after misplacement, dislodgement, or with small Rc and large γi. We compared the performance of the standard catheter-based approach and our robot in these physiologically relevant phantoms.

Accessibility
To access the target region using the standard endovascular neuro-interventional operations, the guidewire is first inserted from the femoral or radial artery and manipulated by pushing and torquing from the operator at the proximal end. After the guidewire is placed, the catheter will be delivered into the vessel coaxially. Due to the longer access route, touristy, and the smaller vessels with thinner vessel walls, catheterization into the distal arteries is often technically challenging 2,7 .
In our experiments conducted with the assistance of an experienced neuroradiologist, we have observed the same phenomenon. We first utilized the combination of the micro guidewire (OD = 0.008 in, ASAHI CHIKAI 008, ASAHI, Japan; denoted as guidewire A hereafter) and medical tubing with the size compatible with the distal MCA (ID = 0.023 in, Medical Tubing, Nordson Medical, USA; denoted as catheter N hereafter) and advanced into the phantoms O and K.
Although the guidewire A could be delivered, co-axial delivery of microcatheters is challenging given the sharp turns (Supplementary Figure 17b). Here we have used glycerol in the lumen to lubricate the inner wall and reduce the kinetic coefficient of frictions (CoF) to a comparable value as the realistic case, i.e., around 0.07 28 (Supplementary Table S2). We

Safety in interaction forces
To quantify the catheter-phantom interaction forces, we utilized the robotic arm's end-effector force and torque sensing function (force resolution: < 0.05 N, Franka Emika, Germany). The phantoms were fixed onto a customized platform, which was connected to the arm's end-effector.
We In contrast, our stent-shaped magnetic soft robot exerted lower forces on the phantoms, which is on the order of 10 -4 to 10 -2 N (Supplementary Figure 18b), according to the validated force modeling. Specifically, there are three groups of interaction forces, i.e., the axial forces applied to the wall at turns due to magnetic pulling force, whose maximum is 5 × 10 -4 N at lmag = 55 mm; the radial forces due to robot deformation, whose maximum is 4.5 × 10 -2 N at the largest deformed state; and the friction forces, whose maximum is 3.6 × 10 -3 N. The maximum forces correspond to the compressive stress of around 5.5 kPa, smaller than the quantified threshold to rupture the endothelial cell at around 12.4 kPa 31,32 .
As stated in the literature 2 and the manual for using the neurovascular guidewire, e.g., ASAHI CHIKAI 008 neurovascular guidewire, "if any resistance is felt during insertion into a catheter used with the guidewire, please do not use it" and "adverse effects of vessel dissection, perforation, and vasospasm etc," the safety of catheterization into these distal regions cannot always be guaranteed given the notable forces. In contrast, given the low interaction forces and no sign of wall deformation observed (Supplementary Figure 18d), our robots could be a promising alternative to enable safer interactions with the vessel walls for therapies in the distal arteries.

Adjustability
The stent-shaped magnetic soft robot could function as an actively-controlled flow diverter to deal with the complications of stent misplacement, dislodgement, and migrations for the therapies of treating wide-neck aneurysms, as we have shown in Figures. 6e -6g.

Supplementary Note 6. Extension to proximal arteries
The  Figures 20d and 20e). Therefore, we utilized this validated model in phantoms and the measured CoFs of porcine arteries (Supplementary Table 2 The same phenomenon also holds for M2 and M3 segments. Based on the above results, we suggest retrievably shape-adaptive locomotion could be feasible using the 50 mm cubic magnet in the proximal region.
Please note that, unlike the distal regions, without proper flow regulations, the wireless locomotion in the proximal region could be unsafe given the high-speed pulsatile flow (e.g., 151 ml/min into the one side M1 segment 26 ) and the small kinetic friction between the robot and the lumen (around 0.07 (Supplementary Table 2)) during the robot movement. The risk can be practically avoided by combining our robot with the balloon guide catheters (BGCs) in the future, which enables the flow arrest during the retrieval of blood clots by stent retrievers or aspiration devices to avoid clots fragment and distal embolization 33 (flow rate was thus regulated to 12 ml/min for all the above investigations on locomotions). However, after the robot stops at the target location and functions as a flow diverter to treat the aneurysm, the flow needs to be recovered, and the robot needs to be self-anchored. Accordingly, we experimentally confirmed that the robot could withstand the realistic flow rate at the rest state. An example result is shown in During the clinical treatment of wide-neck aneurysms, the endovascular stent placement through catheters can divert the flow directly or assist the coiling inside the sac. However, one potential problem of this therapy is stent dislodgement or displacement during the operations 14,15 or migration after the surgery 16 . These fully-deployed stents are nearly impossible to adjust, although some most advanced embolization devices, such as PIPELINE™ FLEX allows resheathable up to two full cycles during the deployment (https://www.medtronic.com/usen/index.html). The current solution to these complications is to either manage the follow-up endovascular operations again to place another stent 16 or conduct the open surgical clipping 14 . In contrast, our stent-shaped wireless magnetic soft robot has the potential to be adjusted directly by magnetic actuation without further implantable devices. As shown above, our quantified experiments on locomotion capability in the phantoms Q -S validate such feasibility. Furthermore, to be more concrete, a new phantom T with physiologically relevant features of the M1 segment (Φl = 2.4 mm -2.7 mm, the radius of curvature Rc = 6 mm) 27 was also fabricated to demonstrate that locomotion around an aneurysm is feasible ( Supplementary Figures 21c and 21d).

Hemocompatibility
The hemocompatibility, including hematotoxicity and thrombogenicity studies, was evaluated using fresh rat blood. We investigated cell morphology by hematoxylin and eosin staining in the hematotoxicity studies. In the thrombogenicity studies, the luciferase assay was conducted to evaluate platelet activation 50  Measurement of platelet activation using luciferase assay. The whole blood sample with collagen-I (100 µg/mL) was used as a positive control (100 %), and the whole blood sample incubated with the Parylene C-coated glass slide was used as a negative control (0 %). The relative ATP release was normalized between the positive control and negative control. Values were compared among the positive control and other groups (***P < 0.001; P = 4.22 × 10 -5 , 1.73 × 10 -5 , and 2.06 × 10 -5 for P-SMP, P-PDMS, and P-glass, respectively) by the one-way ANOVA test. Samples size: 2 mm × 2 mm × 0.1 mm. The data are presented as mean values ± standard deviation for n = 3.

Effects of Parylene C coating on locomotions and functions
We then coated Parylene C on the stent-shaped magnetic soft robot. The effect of Parylene C coating on reducing frictions is notable (Supplementary Figure 26a). Since Parylene C is with high Young's modulus at around 3.2 GPa 51 , we experimentally optimized the robot's stiffness by tuning the robot's Young's modulus Er and the thickness of Parylene C tp, to find the combination that the robot is still flexible enough to fulfill all the locomotion requirements. To satisfy the necessity of tp = 0.5 µm, we currently selected the design with Er = 5.0 MPa (Supplementary Figure 26b).
The experiments indicated that retrievably shape-adaptive locomotion, highly curved route traversing (Rc = 3 mm), and branch traversing (θb = 120°) could be appropriately maintained ( Supplementary Figures 26c -S26e). For the foldable structure, we also experimentally observed that the coating does not influence its shape memory property (Supplementary Figure 26f).

Effect of deformation on the Parylene C coating
The function of the stent-shaped robot depends on its deformation, and these deformations might lead to the fracture of the Parylene C coating layer and exposure of the substrate, which is not ideal for hemocompatibility. To investigate the potential risk, we prepared the Parylene C coated samples for both composites (2 mm × 2 mm × 0.1 mm) and deformed them through bending (strain: 44.7%) and compression (stress: 5.5 kPa), as experienced by the robots during locomotion and functioning. Frictions were ignored due to their low order at 10 -3 N. We then observed the surface

Radial forces
Besides the FEA model, we have also developed a simplified but effective analytical model based on the cantilever beam bending to understand the forces during radial deformation of the soft stent 54 (Supplementary Figure 29a). According to the force analyses on the simplified geometry, Fn can be expressed as where Er is Young's modulus of the robot material, Ib is the second moment of area for the crosssection of a single beam on the composing diamond-shaped cell, lb is the length of the single beam, and Δlc is the change in distance of the two facing beams of the cell under deformation.
To validate these two models, we measured the radial forces   Figure 29c). These measurements agree with both FEA and analytical models with minor offset, which could be resulted from batch-to-batch differentiations in the modulus of the fabricated robot.

Fluidic drag
To validate the modeling of fluidic drag Fdrag, we first experimentally recorded the flow rate that the maximum static friction Ffric,static was overcome, and the robots started to move at each Φl, i.e.,